The present invention relates to a GPS (Global Positioning System) receiver which provides evaluation values for evaluating accuracy of data obtained by GPS measurement, and the invention also relates to a navigation system in which such a GPS receiver is implemented.
In general, a GPS receiver provides data indicative of a position (a GPS position) and a velocity (a GPS velocity), in real time, by performing the GPS measurement. The data (the GPS position and/or the GPS velocity) obtained by performing the GPS measurement is also referred to as a GPS solution. In the GPS measurement, the GPS position is calculated using a range, or a distance between the GPS receiver and GPS satellite, which is measured using a satellite signal.
It is well known that the range measured using the satellite signal includes an error due to, for example, Satellite clock stability, Ephemeris prediction error, Ionospheric delay, Tropospheric delay and other error sources. Therefore, the range measured using satellite signal is called a pseudo-range.
Further, the GPS receiver calculates an evaluation value for evaluating accuracy of the GPS position in real time. In general, 2DRMS (2xc3x97Distance Root Mean Square), i.e., 2"sgr" value (2xc3x97standard deviation) of the horizontal error in the GPS position, is used as the evaluation value. Typically, the 2DRMS is a radius of a circle which contains 95% of all possible GPS positions.
Conventionally, 2DRMS is defined by the equation (1):
2DRMS=2xc2x7HDOPxc2x7"sgr"UERExe2x80x83xe2x80x83(1)
where HDOP is a horizontal dilution of precision, and "sgr"UERE (user equivalent range error) is a root-sum-square value of each 1"sgr" error included in the measured pseudo-range described above. Typically, the "sgr"UERE is a constant, for example, 8.0 m.
The DOP (Dilution Of Precision) is a factor to relate an error in pseudo-range with an error in GPS position. The DOP changes according to the satellite geometry.
In general, a Kalman filter, which is well-known in the art, is employed in the GPS receiver or the navigation system. A publication, xe2x80x9cUnderstanding GPS: principles and applicationsxe2x80x9d, E D. Kaplan ed., Artech House, 1996, describes the use of the Kalman filter in the GPS receiver and calculation of the HDOP and the conventional 2DRMS, teachings of which are incorporated herein by reference.
Treating the GPS solution as a dynamic system, the Kalman filter calculates an estimate of the GPS solution and an error covariance matrix of the estimate. In the mathematical process of the Kalman filter, the estimate and the error covariance matrix of the estimate obtained in the prior estimation are referred to in the succeeding estimation.
The mathematical processes of the Kalman filter includes; provisionally estimating a system state based on a state equation to obtain a provisional estimate; and updating the estimated system state (the estimate) using a difference between a measurement value (a GPS solution) and the provisional estimate.
The updating process for a simple model is given by the equation (2):
X(t)=x(t)+K(t)[Y(t)xe2x88x92x(t)]xe2x80x83xe2x80x83(2)
where X(t) is the estimate, x(t) is the provisional estimate, Y(t) is the measurement value, and K(t) is a Kalman gain.
The following is an example of a computing process in the GPS receiver. The GPS receiver first performs the GPS measurement using the Kalman filter. Next, the HDOP is calculated based on geometry of GPS satellites used in the GPS measurement, and the 2DRMS is calculated according to the equation (1). Then, the GPS solution and the 2DRMS are outputted from the GPS receiver as a part of a GPS message. This GPS message is received and used by the navigation system which functions as a host to the GPS receiver.
In the navigation system, a CPU (Central Processing Unit), which executes a navigation application program, performs estimating a location of a vehicle by using both the GPS solution and a result of a dead-reckoning (a DR solution) computed based on signals outputted by dead-reckoning sensors. The signals from the dead-reckoning sensors include, for example, a gyro output signal, a speed pulse signal and a back signal.
The following is an example of a process of the navigation application program. Initially, the GPS solution and 2DRMS are transferred from the GPS receiver to the CPU in the navigation system. Then, the signals outputted by the dead-reckoning sensors are received and the DR solution is calculated by the CPU. Also, an evaluation value which indicates an error included in the DR solution is calculated.
By making a comparison of the evaluation value of the DR solution and the 2DRMS, the CPU select the GPS solution or the DR solution as a location of the vehicle. Finally, the location selected according to the process described above is compensated using a map-matching.
Thus, the 2DRMS plays an important role in avoiding an undesirable effect from the error included in the DR solution and/or the GPS solution, and in obtaining the location of the vehicle with high accuracy.
However, there may be a case where, the 2DRMS, based on the conventional definition, expressed in the equation (1), takes discrete data values, because the HDOP used for calculating the 2DRMS varies depending on an instantaneous GPS satellites geometry. In particular, in the case of receiving the GPS signal at a mobile station (i.e., a vehicle), since geometry of available satellites, from which GPS signals are receivable, varies from moment to moment, a correlation of the 2DRMS, calculated based on the conventional definition, with respect to time becomes weak.
A complication arises from such nature of the 2DRMS, as follows. FIG. 1 is a graph showing a relation between the 2DRMS based on the conventional definition and a real error 61 included in the GPS solution.
In FIG. 1, relatively long time period of up to t0 represents a state in which the GPS receiver can not receive GPS signals due to the fact that, for example, the vehicle, with which the GPS receiver is equipped, goes through a tunnel. Hereafter, this state is referred to as xe2x80x9con-GPS-measurement-statexe2x80x9d.
At time t0, it becomes possible to receive a plurality of GPS signals (i.e., to use a plurality of GPS satellites) required for performing the GPS measurement, and the GPS receiver obtains navigation data, such as ephemeris. The GPS receiver starts to perform the GPS measurement at t0. Hereafter, this state in which the GPS signals can be received is referred to as xe2x80x9cGPS-measurement-statexe2x80x9d.
That is, FIG. 1 shows progression of 2DRMS and the real error 61 of the GPS solution over time, after the GPS receiver goes into the GPS-measurement-state from the non-GPS-measurement-state.
At time t0, since the Kalman filter does not have historical data (past GPS solutions), the real error included in the GPS solution outputted by the GPS receiver (i.e., the estimate of the Kalman filter) becomes relatively large as shown in FIG. 1. Then, the Kalman filter converges the estimate to a real location of the vehicle with the passage of time. As the estimate converges, accuracy of the estimate increases. Accordingly, the real error 61 included in the estimate decreases.
The 2DRMS can take a low value at time to when the GPS-measurement-state starts because the 2DRMS is a variable which depends on only an instantaneous GPS satellites geometry. The real error 61 falls under the 2DRMS at time t1.
Considering that the navigation system makes the selection described above (i.e., the navigation system selects the GPS solution or DR solution by comparing the evaluation value of DR solution with the 2DRMS) during a time period t0-t1, where the 2DRMS is smaller than the real error 61 (i.e., the 2DRMS does not reflect the real error 61 during the time period t0-t1). In this case, even though real accuracy of the DR solution is higher than real accuracy of the GPS solution, the GPS solution may be selected as a location of the vehicle because the 2DRMS is smaller than the evaluation value of the DR solution.
Such wrong selection causes an accidental jump of a location of a vehicle shown on a map displayed on a monitor screen of the navigation system.
A GPS receiver or a navigation system capable of providing an accurate evaluation value which reflects a real error included in the GPS solution under all condition is required.
It is therefore an object of the invention to provide a GPS receiver or a navigation system capable of calculating an accurate evaluation value which properly reflects a real error included in the GPS solution. A further object of the invention is to provide an improved calculation method for obtaining the accurate evaluation value which properly reflects a real error included in the GPS solution.
For the above object, according to the invention, there is provided a GPS receiver which is provided with a GPS measurement system which performs GPS measurement to obtain a GPS solution, a computing system which provides evaluation values for evaluating errors included in the GPS solution obtained by the GPS measurement, and a modifying system that modifies the evaluation values. The modifying system treats the GPS solution as a dynamic system and modifies the evaluation values in accordance with a system state of the GPS solution in the past. Since the evaluation value is modified according to the past system state of the GPS solution, the past system state can be reflected into the evaluation value. Accordingly, a real error included in the GPS solution can be reflected into the evaluation value under all conditions.
According to another aspect of the invention, there is provided a GPS receiver which is provided with a GPS measurement system which performs GPS measurement to obtain a GPS solution using a Kalman filter, and a computing system which calculates 2DRMS, which is an evaluation value for evaluating an error included in the GPS solution obtained by the GPS measurement, according to an equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(HDOPxc3x97"sgr"UERE+L )2+L )}
wherein, "sgr"H_Kalman represents a horizontal component of an estimate error obtained from a diagonal in an error covariance matrix calculated in a mathematical process of the Kalman filter, HDOP represents a horizontal dilution of precision, and "sgr"UERE represents an user equivalent range error. Since the 2DRMS is a root sum square value of "sgr"H_Kalman and HDOP*"sgr"UERE, a value of "sgr"H_Kalman can be reflected into the 2DRMS. Further, since the "sgr"H_Kalman reflects a past system state of the GPS solution, the past system state can be reflected into the 2DRMS. Accordingly, a real error included in the GPS solution can be reflected into the 2DRMS under all conditions.
According to another aspect of the invention, there is provided a GPS receiver which is provided with an integrating system which performs an integrated positioning, which is an integrated procedure of GPS measurement and dead-reckoning positioning, to obtain an integrated solution using the Kalman filter, and a computing system which calculates 2DRMS, which is an evaluation value for evaluating an error included in the integrated solution obtained by the integrated positioning, according to a first equation:
xe2x80x832DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(HDOPxc3x97"sgr"UERE+L )2+L )}
wherein, "sgr"H_Kalman represents a horizontal component of an estimate error obtained from a diagonal in an error covariance matrix calculated in a mathematical process of the Kalman filter, HDOP represents a horizontal dilution of precision, and "sgr"UERE represents an user equivalent range error. Since the 2DRMS is a root sum square value of "sgr"H_Kalman and HDOP*"sgr"UERE, a value of "sgr"H_Kalman can be reflected into the 2DRMS. Further, since the "sgr"H_Kalman reflects a past system state of the integrated solution, the past system state can be reflected into the 2DRMS. Accordingly, a real error included in the integrated solution can be reflected into the 2DRMS under all conditions.
Preferably, the computing system may calculate 2DRMS, when the GPS receiver is in a state where GPS signals cannot be received, according to a second equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(LastHDOPxc3x97"sgr"UERE+L )2+L )},
wherein LastHDOP indicates HDOP calculated at a time before the GPS receiver being in the state.
Preferably, the integrating system calculates the integrated solutions based only on the dead-reckoning when the GPS receiver being in the state.
According to another aspect of the invention, there is provided a navigation system which is provided with a GPS measurement system which performs GPS measurement to obtain a GPS solution using a Kalman filter, and a computing system which calculates 2DRMS, which is an evaluation value for evaluating an error included in the GPS solution obtained by the GPS measurement, according to an equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(HDOPxc3x97"sgr"UERE+L )2+L )}
wherein, "sgr"H_Kalman represents a horizontal component of an estimate error obtained from a diagonal in an error covariance matrix calculated in a mathematical process of the Kalman filter, HDOP represents a horizontal dilution of precision, and "sgr"UERE represents a user equivalent range error. The navigation system further provided with a position estimating system which estimates positions based on the 2DRMS and the GPS solution obtained by the GPS measurement. Since the "sgr"H_Kalman reflects a past system state of the GPS solution, the past system state can be reflected into the 2DRMS. Accordingly, a real error included in the GPS solution can be reflected into the 2DRMS under all conditions. Accuracy of the positions estimated by the estimating system can be enhanced because the position estimating system estimates the positions using the 2DRMS and GPS solution.
According to another aspect of the invention, there is provided a navigation system which is provided with an integrating system which performs an integrated positioning, which is an integrated procedure of GPS measurement and dead-reckoning positioning, to obtain an integrated solution using the Kalman filter, and a computing system which calculates 2DRMS, which is an evaluation value for evaluating an error included in the integrated solution obtained by the integrated positioning, according to a first equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(HDOPxc3x97UERE+L )2+L )}
wherein, "sgr"H_Kalman represents a horizontal component of an estimate error obtained from a diagonal in an error covariance matrix calculated in a mathematical process of the Kalman filter, HDOP represents a horizontal dilution of precision, and "sgr"UERE represents a user equivalent range error. The navigation system further provided with a position estimating system which estimates positions based on the integrated solution and the 2DRMS calculated according to the first equation. Since the "sgr"H_Kalman reflects a past system state of the integrated solution, the past system state can be reflected into the 2DRMS. Accordingly, a real error included in the integrated solution can be reflected into the 2DRMS under all conditions. Accuracy of the positions estimated by the estimating system can be enhanced because the position stimating system estimates the positions based on the 2DRMS and the integrated solution.
Preferably, the computing system may calculate the 2DRMS, when the navigation system is in a state where GPS signals cannot be received, according to a second equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(LastHDOPxc3x97"sgr"UERE+L )2+L )},
wherein LastHDOP indicates HDOP calculated at a time before the GPS receiver goes into the state. In this case, the position estimating system may use the 2DRMS calculated according to the second equation when the GPS receiver being in the state.
Preferably, the integrating system may calculate the integrated solution based only on the dead-reckoning when the navigation system being in the state.
According to another aspect of the invention, there is provided a method for calculating 2DRMS in a GPS receiver. The method includes calculating the 2DRMS according to a first equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(HDOPxc3x97"sgr"UERE+L )2+L )}
wherein, "sgr"H_Kalman represents a horizontal component of an estimate error obtained from a diagonal in an error covariance matrix calculated in a mathematical process of the Kalman filter, HDOP represents a horizontal dilution of precision, and "sgr"UERE represents a user equivalent range error. Since the 2DRMS is a root sum square value of "sgr"H_Kalman and HDOP*"sgr"UERE, a value of "sgr"H_Kalman can be reflected into the 2DRMS. Further, since the "sgr"H_Kalman reflects a past system state of GPS solution obtained by GPS measurement in the GPS receiver, the past system state can be reflected into the 2DRMS. Accordingly, a real error included in the GPS solution can be reflected into the 2DRMS under all conditions.
Preferably, the calculating step includes calculating the 2DRMS, when the GPS receiver being in a state where GPS signals cannot be received, according to a second equation:
2DRMS=2xc3x97{square root over (("sgr"Hxe2x80x94Kalman+L )2+L +(LastHDOPxc3x97"sgr"UERE+L )2+L )},
wherein LastHDOP indicates HDOP calculated at a time before the GPS receiver goes into the state.